A Trick for Solving Equations with Fractions

Date: 11/12/95 at 23:24:18
From: Anonymous
Subject: similar triangle
Hi,
I already wrote down the equation, and I solved for "y" but I
can't figure out how to do "X".
X+5 = 12+Y = 24
--- ---- --
X 12 18 To get "Y" I first go 12*24=288.
Then I go 288 divided by 18 =16.
16 + 12 =28. (done)
To find "X" I go..........
This is my guess. x+5 = 24
--- --
x 18
1) 24 multiply x to become 24x,and then 18(x+5). So now it's
18x +90 divided by 24x. Now after that I don't know what to do
next.
From Vic

Date: 11/14/95 at 20:21:19
From: Doctor Jeremy
Subject: Re: similar triangle
One trick that comes in handy in cases like this is the fact that:
a c
- = - implies that ad = bc.
b d
You can get that by multiplying both sides by ad.
In your case what that means is from
x+5 24
--- = -- you get 18(x+5)=24x and you can probably take it from there.
x 18
I've used the ad=bc trick so many times in so many cases I do it
without thinking. It's one of those that is often not taught, but
is really useful.
-Doctor Jeremy, The Geometry Forum